In a broader context, our results can be interpreted as empirical evidence for the self-regulating cycle of star formation [1]}.
[2]}, [3]}, [4]} found a tight correlation, called volumetric star formation (VSF) law, between the volume densities of the cold gas and the SFR of nearby disc galaxies.
These volume densities were obtained from the observed surface densities using the gas scale height derived in the same way as here.
The VHE implies that the gas scale height depends on its velocity dispersion, which includes the contributions of thermal motions and turbulence.
The results presented here show that turbulence depends in turn on the SFR.
Hence, we can envision the following self-regulating cycle.
In a quasi-steady state, higher SFR means more turbulence (thicker disc) and lower gas volume density.
According to the VSF law, the SFR declines and turbulence follows, causing the gas volume density to grow again and bringing to a new phase of high SFR.
